A simplified extension of the Crack Analogue model for fretting fatigue with varying normal load

The stress concentration induced by fretting is studied with a simple "Crack Analogue" model (CA), vaguely inspired by the original CA proposed by MIT 20 years ago, "improved" by the first author to take into account simply both contact loads and bulk stresses loads, and even the case of finite stress concentration in the so-called "Crack Like Notch Analogue" (CLNA) model. We suggest here a very crude extension to include the case of varying normal load, where we don't attempt to solve the contact mechanics problem rigorously, only providing an estimate of the equivalent Stress Intensity Factor from the instantaneous load and contact area. Even this results in a problem which has no equivalent in standard fatigue, since it corresponds to a "crack" that is oscillating in size at each cycle. This defines the cycles of stress in the actual material points in the fretted area, but the uncertainties in the approximations suggest that only some limit cases should be approaches this way: for example, when the peaks of tangential load are obtained at about a "mean contact area" (out-of-phase loading) then the original CLNA model could be used.